On 2nd-order fully-nonlinear equations with links to 3rd-order fully-nonlinear equations

TL;DR

This paper explores the conditions under which second-order fully-nonlinear evolution equations are symmetry-integrable and establishes links to third-order equations, advancing understanding of nonlinear evolution equations.

Contribution

It derives general conditions for symmetry-integrability of second-order equations and connects them to third-order equations, providing new insights into nonlinear evolution equations.

Findings

Derived conditions for symmetry-integrability of second-order equations

Established links between second- and third-order fully-nonlinear equations

Identified recursion operators for these classes of equations

Abstract

We derive the general conditions for fully-nonlinear symmetry-integrable second-order evolution equations and their first-order recursion operators. We then apply the established Propositions to find links between a class of fully-nonlinear third-order symmetry-integrable evolution equations and fully-nonlinear second-order symmetry-integrable evolution equations.